Wiener's Nonlinear Expansion Procedure Applied to Cybernetic Problems

In an earlier paper, the author showed how Wiener's Hermite-Laguerre expansion procedure for synthesizing nonlinear functionals could be used to synthesize decision functions for a broad class of continuous stochastic inputs. Furthermore, self-adaptive or learning properties were noted. In the present paper, the relevance of this procedure to cybernetic problems is discussed. In particular, the procedure is applied to the multiple-alternative discrete decision problem with learning characteristic of the recognition processes inherent in adaptive (learning) control. Both sequential and nonsequential procedures are discussed. The resulting model is analogous to a generalized Bayes net type of pattern recognizer or decision maker. However, it is distinguished from the usual Bayes net by rather unique initial conditioning and updating capabilities, its computational or circuit realization, and the fact that its size is determined by rather different considerations from those governing the number of elements in the classical model. Relevant aspects and procedures in cybernetics, intelligence, and learning are discussed and related to the present model. Some problem areas and possible applications worthy of further investigation are discussed.